An apparatus of this kind according to an earlier proposal of the applicant is for example known from the DE-OS 42 23 022. In spite of the fact that in view of the efficiency said construction known from the earlier proposal is forming a so to say continuously working chamber filter press, the necessary constructive expenditure is comparatively high. Further, the hydrostatic dewatering pressure in this known construction is created by the usual pressure pumps which is having certain disadvantages with respect to the delicate handling of the sludge containing a flocculating agent.